The acid hydrolysis of the ether X shown below is fastest when
A
one phenyl group is replaced by a methyl group
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B
one phenyl group is replaced by a para-methoxyphenyl group
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C
two phenyl groups are replaced with two para-methoxyphenyl groups (one apiece)
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D
No structural change is made
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Solution
The correct option is C two phenyl groups are replaced with two para-methoxyphenyl groups (one apiece) The ether has a non-descript alkyl group 'R' on the one side and a triphenylmethyl group on the other side. The oxygen gets protonated and ROH is an excellent leaving group under these conditions. This is because the triphenylmethylium cation is super stable.
Any factor that would improve the stability of the carbocation will make the hydrolysis faster! If any one of the phenyl groups is replaced by a methyl group, the loss of a phenyl group will be destabilizing the intermediate carbocation. This is because the methyl group's hyperconjugation is no match for the highly stabilizing phenyl ring (via conjugation).
Also, replacing a phenyl ring with a para-methoxyphenyl group will have a greater overall stabilizing effect on the intermediate carbocation. This is because the progressive increase in electron density through the carbon chain via the conjugation or resonance of the methoxy oxygen atom. Two such rings will make the reaction go fastest among the given options.